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Author: J S Pinto
Publisher: Elsevier
ISBN: 0857099507
Category : Mathematics
Languages : en
Pages : 270
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Book Description
This modern introduction to infinitesimal methods is a translation of the book Métodos Infinitesimais de Análise Matemática by José Sousa Pinto of the University of Aveiro, Portugal and is aimed at final year or graduate level students with a background in calculus. Surveying modern reformulations of the infinitesimal concept with a thoroughly comprehensive exposition of important and influential hyperreal numbers, the book includes previously unpublished material on the development of hyperfinite theory of Schwartz distributions and its application to generalised Fourier transforms and harmonic analysis. This translation by Roy Hoskins was also greatly assisted by the comments and constructive criticism of Professor Victor Neves, of the University of Aveiro. - Surveys modern reformulations of the infinitesimal concept with a comprehensive exposition of important and influential hyperreal numbers - Includes material on the development of hyperfinite theory of Schwartz distributions and its application to generalised Fourier transforms and harmonic analysis
Author: J S Pinto
Publisher: Elsevier
ISBN: 0857099507
Category : Mathematics
Languages : en
Pages : 270
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Book Description
This modern introduction to infinitesimal methods is a translation of the book Métodos Infinitesimais de Análise Matemática by José Sousa Pinto of the University of Aveiro, Portugal and is aimed at final year or graduate level students with a background in calculus. Surveying modern reformulations of the infinitesimal concept with a thoroughly comprehensive exposition of important and influential hyperreal numbers, the book includes previously unpublished material on the development of hyperfinite theory of Schwartz distributions and its application to generalised Fourier transforms and harmonic analysis. This translation by Roy Hoskins was also greatly assisted by the comments and constructive criticism of Professor Victor Neves, of the University of Aveiro. - Surveys modern reformulations of the infinitesimal concept with a comprehensive exposition of important and influential hyperreal numbers - Includes material on the development of hyperfinite theory of Schwartz distributions and its application to generalised Fourier transforms and harmonic analysis
Author: J S Pinto
Publisher: Horwood Publishing
ISBN: 9781898563990
Category : Mathematics
Languages : en
Pages : 274
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Book Description
The most important material in the book is a hyperfinite theory of Schwartz distributions with applications to generalised Fourier transforms and harmonic analysis, and is not available in any other text on nonstandard methods."--Jacket.
Author: John L. Bell
Publisher: Cambridge University Press
ISBN: 0521887186
Category : Mathematics
Languages : en
Pages : 7
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Book Description
A rigorous, axiomatically formulated presentation of the 'zero-square', or 'nilpotent' infinitesimal.
Author: E.I. Gordon
Publisher: Springer Science & Business Media
ISBN: 940170063X
Category : Mathematics
Languages : en
Pages : 435
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Book Description
Infinitesimal analysis, once a synonym for calculus, is now viewed as a technique for studying the properties of an arbitrary mathematical object by discriminating between its standard and nonstandard constituents. Resurrected by A. Robinson in the early 1960's with the epithet 'nonstandard', infinitesimal analysis not only has revived the methods of infinitely small and infinitely large quantities, which go back to the very beginning of calculus, but also has suggested many powerful tools for research in every branch of modern mathematics. The book sets forth the basics of the theory, as well as the most recent applications in, for example, functional analysis, optimization, and harmonic analysis. The concentric style of exposition enables this work to serve as an elementary introduction to one of the most promising mathematical technologies, while revealing up-to-date methods of monadology and hyperapproximation. This is a companion volume to the earlier works on nonstandard methods of analysis by A.G. Kusraev and S.S. Kutateladze (1999), ISBN 0-7923-5921-6 and Nonstandard Analysis and Vector Lattices edited by S.S. Kutateladze (2000), ISBN 0-7923-6619-0
Author: Ieke Moerdijk
Publisher: Springer Science & Business Media
ISBN: 147574143X
Category : Mathematics
Languages : en
Pages : 401
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Book Description
The aim of this book is to construct categories of spaces which contain all the C?-manifolds, but in addition infinitesimal spaces and arbitrary function spaces. To this end, the techniques of Grothendieck toposes (and the logic inherent to them) are explained at a leisurely pace and applied. By discussing topics such as integration, cohomology and vector bundles in the new context, the adequacy of these new spaces for analysis and geometry will be illustrated and the connection to the classical approach to C?-manifolds will be explained.
Author: Abraham Robinson
Publisher: Princeton University Press
ISBN: 1400884225
Category : Mathematics
Languages : en
Pages : 315
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Book Description
Considered by many to be Abraham Robinson's magnum opus, this book offers an explanation of the development and applications of non-standard analysis by the mathematician who founded the subject. Non-standard analysis grew out of Robinson's attempt to resolve the contradictions posed by infinitesimals within calculus. He introduced this new subject in a seminar at Princeton in 1960, and it remains as controversial today as it was then. This paperback reprint of the 1974 revised edition is indispensable reading for anyone interested in non-standard analysis. It treats in rich detail many areas of application, including topology, functions of a real variable, functions of a complex variable, and normed linear spaces, together with problems of boundary layer flow of viscous fluids and rederivations of Saint-Venant's hypothesis concerning the distribution of stresses in an elastic body.
Author: James M. Henle
Publisher: Courier Corporation
ISBN: 0486151018
Category : Mathematics
Languages : en
Pages : 146
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Book Description
Introducing calculus at the basic level, this text covers hyperreal numbers and hyperreal line, continuous functions, integral and differential calculus, fundamental theorem, infinite sequences and series, infinite polynomials, more. 1979 edition.
Author: Siu-Ah Ng
Publisher: World Scientific
ISBN: 9812564527
Category : Business & Economics
Languages : en
Pages : 313
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Book Description
At the beginning of the new millennium, two unstoppable processes aretaking place in the world: (1) globalization of the economy; (2)information revolution. As a consequence, there is greaterparticipation of the world population in capital market investment, such as bonds and stocks and their derivatives
Author: David J. Briggs
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
Author: Ernest William Hobson
Publisher:
ISBN:
Category : Infinite
Languages : en
Pages : 48
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Book Description
